OK, I've tried to nail this one down for a while and I think I've done it.
Tyrell, Ser Loras -
Quote
“Ser Loras was the youngest son of Mace Tyrell, the Lord of Highgarden and Warden of the South. At sixteen, he was the youngest rider on the field, yet he had unhorsed three knights of the Kingsguard that morning in his first three jousts.” (AGoT 249)
Sansa looking on Ser Loras at the Hand’s tourney, before Arya overhears Varys with Illyrio, so it is still in 298 when this takes place.
Quote
“‘How old are you, Ser Loras?’ Tyrion asked him.
‘Seventeen, my lord’
Seventeen, and beautiful, and already a legend. Half the girls in the Seven Kingdoms want to bed him, and all the boys want to be him. ‘If you pardon my asking, ser - why would anyone choose to join the Kingsguard at seventeen?’
‘Prince Aemon the Dragonknight took his vows at seventeen,’ Ser Loras said, ‘and your brother Jaime was younger still.’
‘I know their reasons. What are your? The honor of serving beside such paragons as Meryn Trant and Boros Blunt?’ He gave the boy a mocking grin. ‘To guard the king’s life, you surrender your own. You give up your lands and titles, give up hope of marriage, children ...’
‘House Tyrell continues through my brothers,’ Ser Loras said. ‘It is not necessary for a third son to wed, or breed.’
‘Not necessary, but some find it pleasant. What of love?’
‘When the sun has set, no candle can replace it.’
‘Is that from a song?’ Tyrion cocked his head, smiling. ‘Yes, you are seventeen, I see that now.’
Ser Loras tensed. ‘Do you mock me?’
A prickly lad. ‘No. If I’ve given offense, forgive me. I had my own love once, and we had a song as well.’ (ASoS 137)
Tyrion talking to Ser Loras after the Imp has recovered from his wounds at the Battle of the Blackwater and before the wedding of Joffrey and Margaery - so, in Year 299.
Quote
“‘Seventeen and a knight of the Kingsguard,’ said Jaime. ‘You must be proud. Prince Aemon the Dragonknight was seventeen when he was named. Did you know that?’” (ASoS 758)
Jaime talking to Ser Loras in the White Tower after Joffrey’s assassination. If this is read as meaning Ser Loras is seventeen at this point in the story then it proves him to have been born in Year 282 because he is both seventeen in 299 and 300.
The other reading, one having the reference being a look back to when Ser Loras was admitted to the Kingsguard, would have him as turning 18 in 299 so we still have these two possibilities:
{A} -- Ser Loras is 15 turning 16 in 298; 16 turning 17 in 299, and 17 turning 18 in 300, or
{B} -- Ser Loras is 16 turning 17 in 298; 17 turning 18 in 299, and 18 turning 19 in 300.
I think this settles it, especially when combined with the likely reading of the above quote.
Quote
“Ser Loras was a year older than his sister,but they had the same big brown eyes, the same thick brown hair falling in lazy ringlets to their shoulders, the same smooth unblemished skin.” (AFfC 182)
Cersei looking at Ser Loras at Tommen and Margaery’s wedding in Year 300 when Margaery is still 16 - this should mean option A is the only viable option since in option B Loras would be 18 when his 16 year old sister is marrying Joffrey. A clear contradiction to Cersei’s comment about his being
a year older than Margaery at the time.
This means Ser Loras was born in Year 282.